RSS Leeds

RSS Leeds/Bradford group16 April 2008 The D/L method: 11 years on : 

RSS Leeds/Bradford group16 April 2008 The D/L method: 11 years on Frank Duckworth Editor, RSS NEWS

The D/L method : 

The D/L method why it was needed how it works how it came into use experience with operation questions ???

features of one-day cricket : 

features of one-day cricket one innings per side limited overs (eg 50/innings) maximum N/5 overs per bowler field placing restrictions more flexible playing conditions negative play penalised matches cannot be drawn

One-day cricket’s major problem... : 

One-day cricket’s major problem...

Structure of one-day cricket : 

Structure of one-day cricket sides perform in turn Team 1 have 50 overs and 10 wickets Team 2 have to beat Team 1’s score with same resources Problem: how do you correct for one side losing overs?

Target correction by average run rate : 

Target correction by average run rate Team 1: 250 in 50 overs Rain during interval: Team 2 given 25 Team 2’s target = 250 x 25/50 = 125 (+1) in 25 is this equivalent to 250 in 50 ? or to 500 in 100 ? or to 1000 in 200 ?

Timing of stoppage : 

Timing of stoppage Team 1: 250 in 50 overs Team 2: 124/0 in 25 match abandoned due to rain: LOST! Team 2: 126/9 in 25 match abandoned due to rain: WON!

Australian rain ruleif Team 2 lose overs due to rain so only have N2 overs, their target is calculated from the N2 most productive overs in Team 1’s innings : 

Australian rain ruleif Team 2 lose overs due to rain so only have N2 overs, their target is calculated from the N2 most productive overs in Team 1’s innings Example 1: Team 1 make 200 all out in 30 overs Without rain, Team 2’s target is 201 in 50 overs Rain gives Team 2 only 30 overs: target is same Example 2: Team 1 make 100 all out in 25 overs Team 2 reach 99/0 in 25 overs: and then in rains Result: they LOSE!

World Cup 1992 : 

World Cup 1992 Semi-final: South Africa v England, Sydney (reduced to 45 overs/side) England: 252/6 in 45 South Africa: 231/6 in 42.5 needed 22 to win from 2.1 overs (13 balls) Rain caused loss of 2 overs Target reduced by cheapest 2 overs England faced 2 maiden overs: so credit for lost overs = 0 Now needed 22 runs from 0.1 over (1 ball)

Wayne’s data - 1991 English season : 

Wayne’s data - 1991 English season y(x) = bx + cx2

D/L methodKey stages in development : 

D/L methodKey stages in development Sept 1992 RSS conference, Sheffield 1993-4 UWE student project Oct 1995 presentation to TCCB

Duckworth/Lewis formula : 

Duckworth/Lewis formula Z(u,w) = Z0F(w) [1 – exp –bu/F(w)] Z = average number of further runs scored u = overs remaining w = wickets fallen

Duckworth/Lewis formula : 

Duckworth/Lewis formula Z(u,w) = Z0F(w) [1 – exp –bu/F(w)] Z = average number of further runs scored u = overs remaining w = wickets fallen {∂Z/∂u}u=0 = bZ0

D/L method – Example 1 : 

D/L method – Example 1 Team 1 make 250 in 50 overs Team 2: 100/0 in 25 overs rain washes out rest of innings resources remaining: 25 overs left all wkts intact (0 lost) resources left = 68.7% resources lost = 68.7% resources available = 31.3% score to beat = 31.3% of 250 = 78.25 par score = 78 Team 2 are ahead of par by 22 runs Team 2 win by 22 runs

D/L method – Example 2 : 

D/L method – Example 2 Team 1 make 250 in 50 overs Team 2: 130/9 in 25 overs rain washes out rest of innings resources remaining: 25 overs left 1 wkt intact (9 lost) resources left = 7.6% resources lost = 7.6% resources available = 92.4% score to beat = 92.4% of 250 = 231 par score = 231 Team 2 are 101 runs behind par Team 1 win by 101 runs

D/L method – Example 3 : 

D/L method – Example 3 Team 1 make 250 in 50 overs rain during interval: Team 2 given 25 overs resources remaining: 25 overs left all wkts intact (0 lost) resources left = 68.7% resources available = 68.7% score to beat = 68.7% of 250 = 171.75 Team 2’s target = 172 in 25 overs

D/L method – Example 4 : 

D/L method – Example 4 Team 1 make 200 in 50 overs Team 2: 110/5 in 30 overs rain causes loss of 5 overs resources remaining before rain: 20 overs left 5 wkts intact (5 lost) resources left = 40% resources remaining after rain: 15 overs left 5 wkts intact (5 lost) resources left = 35% resources lost due to rain = 5% resources available = 95% score to beat = 95% of 200 = 190 target = 191 from 45 overs

D/L method – Example 5 : 

D/L method – Example 5 Team 1 make 110/5 in 30 overs; it rains innings closed: Team 2 allocated 30 overs When Team 1’s innings curtailed, resources remaining: 20 overs left; 5 wkts intact (5 lost) resources left = 40% resources lost = 40% resources available = 60% When Team 2 start their innings, resources remaining: 30 overs left; all wkts intact (0 lost) resources left = 77.1% resources available = 77.1% Team 2 have 77.1%: Team 1 have 60% (17% less) Team 2 given enhanced target enhancement = 17.1% of 235 = 40 runs

D/L method of target revision : 

D/L method of target revision read from table resources remaining when play stops read from table resources remaining when play resumes subtraction gives resources lost set target by comparing resources available to each team

Adoption of D/L method : 

Adoption of D/L method July 1996 presentation to ICC Nov 1996 presentation to ECB – success! Oct 1996 adoption by Zimbabwe 1 Jan 1997 first use in Zimbabwe

Zimbabwe v EnglandHarare 1 Jan 1997 : 

Zimbabwe v EnglandHarare 1 Jan 1997 Zimbabwe: 200 off 50 overs 8 overs lost before start of England's innings England’s target 92.5% of 200 = 185 in 42 overs England made 179 and lost by 6 runs (ARR target = 42/50 x 200 = 168)

: 

“if it is interrupted by rain, a new system will be used. … Anyone rash enough to try to understand it while nursing a new year hangover will soon be reaching out again for the aspirin” Simon Wilde The Times 1 Jan 1997

: 

“ this one – so indeciferable (sic) that the Admiralty might be interested in it for a new secret code – is the brainchild of the Royal Statistical Society’s magazine’s editor and a university mathematics boffin, and coughed up a revised target of 185” Martin Johnson The Daily Telegraph 2 Jan 1997

Spread of D/L world-wide : 

Spread of D/L world-wide Oct 96 adoption by Zimbabwe Dec 96 adoption by ECB Mar/Ap 97 ICC Trophy in Malaysia Dec 97 New Zealand Sept 98 South Africa Oct 98 Pakistan & India Nov 98 West Indies May 99 World Cup (in England) Aug 99 rest of world (Sri Lanka/Australia) May 01 formal adoption by ICC Feb/Mar 03 World Cup (South Africa) Oct 03 Professional Edition in ODIs

World-wide use of D/L(to 13 April 2008) : 

World-wide use of D/L(to 13 April 2008) England & Wales 361 Sri Lanka 100 South Africa 98 Australia 60 West Indies 48 New Zealand 39 Zimbabwe 30 Ireland 29 Pakistan 29 Malaysia 19 Canada 14 others 35 Total 862

Reasons for D/L invocation(to 31 March 2008) : 

Reasons for D/L invocation(to 31 March 2008) rain or bad light 837 floodlight failure 18 crowd disturbance 3 sandstorm 1 snow 1 sun ! 2 total 862

Change to Professional Edition(examples of limitations of current method) : 

Change to Professional Edition(examples of limitations of current method) Example 1: extreme case Team 1 score 1800 in 50 overs Team 2 given 25 overs Team 2 have 68.7% of Team 1’s resources Target = 0.687 x 1800 = 1237 (>8/ball)

Change to Professional Edition(examples of limitations of current method) : 

Change to Professional Edition(examples of limitations of current method) Example 2: 2003 WC final: Australia v India Australia made 359 in their 50 overs India were 145/3 in 23 overs: rain was threatening par score = 149 if … it rained after 25 overs India didn’t lose a wicket in next 2 overs India gained a further 5 runs on par then … India would have won!

The Professional Edition : 

The Professional Edition Z(u,0,λ) = Z0F(w) λn(w)+1 {1 – exp(-bu/[λn(w)F(w)])}

Further information : 

Further information tables: http://icc-cricket.yahoo.com/ booklet: Acumen Books, 01782 720753, or www.acumenbooks.co.uk other queries: f.duckworth@rss.org.uk